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Implicit differentiation is the procedure of differentiating an implicit equation with respect to the desired variable x while treating the other variables as unspecified ...

"Implies" is the connective in propositional calculus which has the meaning "if A is true, then B is also true." In formal terminology, the term conditional is often used to ...

An improper integral is a definite integral that has either or both limits infinite or an integrand that approaches infinity at one or more points in the range of ...

A generalization of the complete beta function defined by B(z;a,b)=int_0^zu^(a-1)(1-u)^(b-1)du, (1) sometimes also denoted B_z(a,b). The so-called Chebyshev integral is given ...

The "complete" gamma function Gamma(a) can be generalized to the incomplete gamma function Gamma(a,x) such that Gamma(a)=Gamma(a,0). This "upper" incomplete gamma function is ...

A conic section that is tangent to all sides of a triangle is called an inconic. Any trilinear equation of the form ...

A function f(x) increases on an interval I if f(b)>=f(a) for all b>a, where a,b in I. If f(b)>f(a) for all b>a, the function is said to be strictly increasing. Conversely, a ...

A non-zero module which is not the direct sum of two of its proper submodules. The negation of indecomposable is, of course, decomposable. An abstract vector space is ...

Assume X, Y, and Z are lotteries. Denote "X is preferred to Y" as X≻Y, and indifference between them by X∼Y. One version of the probability axioms are then given by the ...

An independent variable is a variable whose values don't depend on changes in other variables. This is in contrast to the definition of dependent variable. As with dependent ...